Subgroups — C₃₁×#496 #14520677

Order 1984.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
2	C₂×D₈×C₃₁	C₂	1	2	yes	maximal, complemented
3	C₃₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₃₁	—	2	2	no	—
8	C₂×D₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×D₄×C₃₁	C₂²	1	2	yes	—
10	SD₁₆×C₃₁	—	2	4	no	—
11	D₈×C₃₁	—	2	4	no	—
12	C₂×C₈×C₃₁	C₂²	1	2	yes	—
13	C₂²⋊C₄×C₃₁	—	2	2	no	—
14	C₄²×C₃₁	C₂²	1	1	yes	characteristic
15	C₂³×C₃₁	—	2	1	no	—
16	C₂³×C₃₁	—	2	2	no	—
17	Q₈×C₃₁	—	2	2	no	—
18	D₄×C₃₁	—	2	2	no	—
19	D₄×C₃₁	—	2	2	no	—
20	D₄×C₃₁	—	2	2	no	—
21	D₄×C₃₁	—	4	4	no	—
22	C₂×C₄×C₃₁	—	2	1	no	—
23	C₂×C₄×C₃₁	D₄	1	2	yes	—
24	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
25	C₈×C₃₁	D₄	1	4	yes	complemented
26	C₂²×C₃₁	—	4	1	no	—
27	C₂²×C₃₁	—	4	2	no	—
28	C₂²×C₃₁	—	4	4	no	—
29	C₂²×C₃₁	—	4	2	no	—
30	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₃₁	—	2	2	no	—
32	C₄×C₃₁	—	4	1	no	—
33	C₄×C₃₁	C₂×D₄	1	2	yes	—
34	#496	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂×C₃₁	—	8	2	no	—
36	C₂×C₃₁	—	8	1	no	—
37	C₂×C₃₁	#127	1	1	yes	characteristic
38	C₂×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
39	C₂×SD₁₆	C₂×C₃₁	1	2	yes	complemented
40	C₂×D₈	C₂×C₃₁	1	2	yes	complemented
41	#127	C₂×C₃₁	1	1	yes	characteristic, complemented
42	#124	C₂×C₃₁	1	1	yes	characteristic, complemented
43	#97	C₂×C₃₁	1	1	yes	characteristic, complemented
44	C₃₁	#496	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×Q₈	C₂²×C₃₁	1	1	yes	characteristic
46	C₂×D₄	—	2	2	no	—
47	C₂×D₄	C₂²×C₃₁	1	1	yes	characteristic
48	C₂×D₄	C₂²×C₃₁	1	2	yes	—
49	SD₁₆	—	2	4	no	—
50	D₈	—	2	4	no	—
51	C₂×C₈	C₂²×C₃₁	1	2	yes	—
52	C₂²⋊C₄	—	2	2	no	—
53	C₄²	C₂²×C₃₁	1	1	yes	characteristic
54	C₂³	—	2	1	no	—
55	C₂³	—	2	2	no	—
56	Q₈	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	2	2	no	—
59	D₄	—	2	2	no	—
60	D₄	—	4	4	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	D₄×C₃₁	1	2	yes	—
63	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
64	C₈	D₄×C₃₁	1	4	yes	complemented
65	C₂²	—	4	1	no	—
66	C₂²	—	4	2	no	—
67	C₂²	—	4	4	no	—
68	C₂²	—	4	2	no	—
69	C₂²	C₂×D₄×C₃₁	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	4	1	no	—
72	C₄	C₂×D₄×C₃₁	1	2	yes	—
73	C₂	—	8	2	no	—
74	C₂	—	8	1	no	—
75	C₂	C₃₁×#127	1	1	yes	characteristic
76	C₂	C₃₁×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×SD₁₆×C₃₁	C₂	semidirect
2. C₂×D₈×C₃₁	C₂	semidirect
3. C₃₁×#127	C₂	semidirect
4. C₃₁×#124	C₂	semidirect
5. C₃₁×#97	C₂	semidirect
25. C₈×C₃₁	D₄	semidirect
34. #496	C₃₁	direct (N × H)
39. C₂×SD₁₆	C₂×C₃₁	semidirect
40. C₂×D₈	C₂×C₃₁	semidirect
41. #127	C₂×C₃₁	semidirect
42. #124	C₂×C₃₁	semidirect
43. #97	C₂×C₃₁	semidirect
44. C₃₁	#496	direct (N × H)
64. C₈	D₄×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×SD₁₆×C₃₁	2
C₂×D₈×C₃₁	2
C₃₁×#127	2
C₃₁×#124	2
C₃₁×#97	2
#496	31

Subgroups — C31×#496 #14520677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#496 #14520677